José Fernando Gonçalves

Abstract
This paper addresses a two-dimensional (2D) non-guillotine cutting problem, where a set of small rectangular items of given types has to be cut from a large rectangular stock plate having defective regions so as to maximize the total value of the rectangles cut. The number of small items of each item type which can be cut from the large object is unrestricted. A novel MIP model and a hybrid approach combining a novel placement procedure with a biased random-key genetic algorithm (BRKGA) are presented. The parameters used by the novel placement procedure for the development of a cutting plan are evolved by the BRKGA. The management of the free spaces and of the defects uses a maximal-space representation. The approach is evaluated and compared to other approaches by means of a series of detailed numerical experiments using 5414 benchmark instances taken from the literature. The experimental results validate the quality of the solutions and the effectiveness of the proposed algorithm.

Abstract
Background: This work addresses the maximum edge weight clique problem (MEWC), an important generalization of the well-known maximum clique problem. Methods: The MEWC problem can be used to model applications in many fields including broadband network design, computer vision, pattern recognition, and robotics. We propose a random key genetic algorithm to find good quality solutions for this problem. Computational experiments are reported for a set of benchmark problem instances derived from the DIMACS maximum clique instances. Results: The results obtained show that our algorithm is both effective and efficient, as for most of the problem instances tested, we were able to match the best-known solutions with very small computational time requirements. © 2018 Bentham Science Publishers.

Abstract
This paper proposes an adaptive Biased Random-key Genetic Algorithm (A-BRKGA), a new method with on-line parameter control for combinatorial optimization problems. A-BRKGA has only one problem-dependent component, the decoder and all other parts can be reused. To control diversification and intensification, a novel adaptive strategy for parameter tuning is introduced. This strategy is based on deterministic rules and self adaptive schemes. For exploitation of specific regions of the solution space we propose a local search in promising communities. The proposed method is evaluated on the Capacitated Centered Clustering Problem (CCCP), which is an NP-hard problem where a set of n points, each having a given demand, is partitioned into m clusters each with a given capacity. The objective is to minimize the sum of the Euclidean distances between the points and their geometric cluster centroids. Computational results show that the A-BRKGA with local search is competitive with other methods of literature.

Abstract
A random-key genetic algorithm is an evolutionary metaheuristic for discrete and global optimization. Each solution is encoded as an array of n random keys, where a random key is a real number, randomly generated, in the continuous interval [0,1] A decoder maps each array of random keys to a solution of the optimization problem being solved and computes its cost. The algorithm starts with a population of p arrays of random keys. At each iteration, the arrays are partitioned into two sets, a smaller set of high-valued elite solutions and the remaining nonelite solutions. All elite elements are copied, without change, to the next population. A small number of random-key arrays (the mutants) are added to the population of the next iteration. The remaining elements of the population of the next iteration are generated by combining, with the parametrized uniform crossover of Spears and DeJong (On the virtues of parameterized uniform crossover. In: Proceedings of the fourth international conference on genetic algorithms, San Mateo, pp 230-236, 1991), pairs of arrays. This chapter reviews random-key genetic algorithms and describes an effective variant called biased random-key genetic algorithms.

Abstract
This chapter introduces biased random-key genetic programming, a new metaheuristic for evolving programs. Each solution program is encoded as a vector of random keys, where a random key is a real number randomly generated in the continuous interval [0,1]. A decoder maps each vector of random keys to a solution program and assigns it a measure of quality. A Program-Expression is encoded in the chromosome using a head-tail representation which is later transformed into a syntax tree using a prefix notation rule. The artificial simulated evolution of the programs is accomplished with a biased random-key genetic algorithm. Examples of the application of this approach to symbolic regression are presented.